JP2972047B2 - Sweep solid generator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to shape processing such as computer-aided design (CAD) and computer-aided production (CAM), and more particularly, to a swept solid generator for generating a swept surface.

[0002]

2. Description of the Related Art As a conventional technique, when a trajectory curve is divided into a plurality of lines in a CAD system, the trajectory curve is converted into one free curve, and the trajectory curve is reduced to one to perform a sweep solid generation process. I was

Another conventional technique is disclosed in Japanese Unexamined Patent Publication No.
In the “3D three-dimensional shape generating device” described in JP-117572A, coordinate conversion is performed based on a tangent vector and a curvature vector at a point on a trajectory curve,
An interpolated curve was generated, and a sweep solid was generated by interpolating the feature curve and the interpolated curve with a Gregory Patch.

[0004]

However, in the above-described method of converting a plurality of trajectory curves used in the conventional CAD system into one free curve, there is only one characteristic curve. Although there is an advantage that the time algorithm can be achieved by one, for example,
Sections that can clearly generate a sweep solid from the type of orbital curve, such as straight lines and arcs, are also treated as free curves, so the amount of data defining the sweep solid increases, the processing load increases, and processing becomes unstable. There was a problem.

[0005] In the above-mentioned "tertiary three-dimensional shape generating apparatus",
A sweep surface obtained in a portion where the curvature changes greatly has a problem that the surface is extremely twisted, and a generated sweep solid is divided into small patches due to the nature of the used surface. The surface equation described in the “cubic three-dimensional shape generation device” is a new surface equation that solves the problem that has conventionally occurred when generating a surface that smoothly connects to an adjacent surface. There was a problem that compatibility was required.

SUMMARY OF THE INVENTION An object of the present invention is to generate a swept solid reflecting the characteristics of an orbital curve without being affected by torsion caused by a sharp change in curvature, and to express a synthesized swept solid in a general curved surface format. The present invention provides a sweep solid generator capable of performing the above-described operations.

[0007]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a characteristic curve calculating means for calculating a characteristic curve at an arbitrary point on a trajectory curve, and a feature for disposing the calculated characteristic curve at both ends of the trajectory curve. Curve arranging means, solid generating method judging means for judging whether or not to use an approximation method in the generation of a swept solid based on a trajectory curve and characteristic curves arranged at both end points of the trajectory curve, and solid generating method judging means In the case where it is determined that the approximation method is not used in the generation of the sweep solid, the section sweep solid generation means for generating the sweep solid based on the trajectory curve and the characteristic curve, and the generation of the sweep solid by the solid generation method determination means. An approximate section sweep solid generating means for appropriately adding a characteristic curve to the trajectory curve using a characteristic curve calculating means when it is determined that the approximating method is to be used, and approximately generating a solid; A section matching means for adjusting connectivity between adjacent solids in the section sweep solid obtained by the solid generating means and the approximate section sweep solid generating means, and a solid synthesizing means for synthesizing the section sweep solid into one sweep solid. Is achieved by a sweep volume generator.

[0008]

The sweep solid generating apparatus of the present invention sweeps by moving or rotating one or a plurality of orbital curves arranged in a space and a characteristic curve from one or a plurality of characteristic curves along the orbital curve. To generate a surface,
Using a characteristic curve calculating means for calculating a characteristic curve at an arbitrary point of the orbit curve, the characteristic curve is arranged at both end points and inflection points of each orbit curve, and in each orbit curve section, arranged at both ends of the section. Based on the obtained characteristic curve and the trajectory curve, it is determined whether or not an approximation method is necessary for the generation means of the sweep three-dimensional generation. Generate a swept solid based on the orbit curve. When it is determined that the approximation method is necessary, the characteristic curve is appropriately added to the trajectory curve using the characteristic curve calculation means by the approximate sweep solid generation means, and the solid is approximately generated. The generated section sweep solid is adjusted to the connectivity between the adjacent solids and combined into one sweep solid. Further, the characteristic curve calculating means calculates a characteristic curve according to the type of the trajectory curve,
If the coordinate transformation matrix used for calculation cannot be uniquely defined, specify an appropriate plane, and calculate the coordinate transformation matrix at the parameter points based on the normal vector of the plane and the tangent vector at any parameter point of the trajectory curve. Define. In the section sweep solid generating means,
A section sweep solid corresponding to the type of the orbit curve is generated.
The approximate section swept solid generating means compares the sectional curve at an arbitrary parameter point of the section swept solid with the curve calculated at the parameter point using the characteristic curve calculating means.

[0009]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing a configuration of a sweep solid generator according to the present invention.

FIG. 1 is a block diagram showing the configuration of an embodiment of a sweep solid generator according to the present invention.

The sweep solid generator of FIG. 1 includes a control unit 1, a display unit 2 connected to the control unit 1, a keyboard unit 3 connected to the control unit 1, a tablet unit 4 connected to the control unit 1, A file section 5 connected to the section 1; a modeling section 6 connected to the control section 1; a feature curve arrangement section 7 connected to the control section 1; a characteristic curve calculation section 8 connected to the feature curve arrangement section 7; A three-dimensional generation method determining unit 9 connected to the unit 1;
Section sweep solid generating section 10 connected to solid generating method determining section 9, approximate section sweep generating section 11 connected to solid generating method determining section 9 and characteristic curve calculating section 8, and matching between curved surfaces connected to control section 1 It comprises a unit 12 and a three-dimensional synthesizing unit 13 connected to the control unit 1.

Next, referring to the flowchart of FIG.
The operation of each of the above components will be described.

First, as shown in FIG. 3, one or a plurality of trajectory curves and one or a plurality of characteristic curves are input to the modeling unit 6 (step S1). Next, the characteristic curve input unit 7 arranges the characteristic curves input using the characteristic curve calculation unit 8 at both end points and inflection points of the trajectory curve as shown in FIG. 4 (step S2). At that time, the characteristic curve calculation unit 8 uses a method for sweeping the characteristic curve or a calculation method according to the type of the trajectory curve. For example, when calculating the characteristic curve while maintaining the angle between the characteristic curve and the trajectory curve, when the trajectory curve is a straight line, the calculation is performed using a parallel movement method, and when the trajectory curve is a circular arc, the rotation movement method is used. Is calculated using When the trajectory curve is a free curve, after dividing at the inflection point, a plane is designated in the division section, a coordinate transformation matrix is generated based on the designated plane, and a characteristic curve is calculated.

As shown in FIG. 5, the plane designating method is a method of uniformly designating a plane in any section, and as shown in FIG. 6, in each divided section, an end point and a middle point of the section are used. There is a method for determining the plane. In this case, when a plane cannot be determined at three points, the section is determined to be a straight line, and a characteristic curve is calculated using a parallel movement method.

Once the plane is determined, the cross product is calculated by using the tangent vector at each point and the normal vector of the plane at the point of the characteristic curve on the trajectory curve and the characteristic curve calculation destination point. Let it be the main normal vector. Subsequently, an outer product is obtained by using the main normal vector and the tangent vector, and the result is used as the triangular vector.

As shown in FIG. 7, a coordinate transformation matrix between two points is calculated using the tangent vector, the main normal vector, and the triangular vector thus obtained as a coordinate system, and coordinate transformation is performed. Is calculated as follows.

In the case of sweeping the characteristic curves in parallel, the calculation is performed using a parallel movement method regardless of the type of the orbit curve. Therefore, the arrangement is as shown in FIG.

As shown in FIG. 10, when sweeping is performed by using characteristic curves having different shapes, as shown in FIG. 11, two points on both sides of the calculation destination point are calculated at the calculation destination point for calculating the characteristic curve. Calculating each characteristic curve at the calculation destination point based on the characteristic curve, and then linearly interpolating the calculated two curves by the ratio of the length from each point where the original characteristic curve is arranged to the calculation destination point Perform

As shown in FIG. 12, a curve obtained by linear interpolation is used as a characteristic curve at a calculation destination point.

After arranging the characteristic curves at the end points and inflection points of the trajectory curve, a section sweep solid is generated in each trajectory curve section based on the trajectory curve and the characteristic curve (step S3). The three-dimensional generation method determining unit 9 determines whether or not to generate the section sweep solid based on the characteristic curve and the trajectory curve, and when it is determined that the three-dimensional solid can be generated, the section sweep three-dimensional generator 10 generates the section sweep solid.

For example, as shown in FIG. 13, when the trajectory curve is a straight line, a section-swept solid can be generated by using a ruled surface generation method. In addition, as shown in FIG. 14, when an arc is a trajectory curve and the shapes of the characteristic curves at both ends of the arc match, section sweep solid generation can be performed using a solid generation method around the arc.

If it is determined by the three-dimensional generation method discriminating unit 9 that it is not possible to generate the section sweep solid, the approximate section sweep three-dimensional generator 11 generates the section sweep solid. For example, as shown in FIG. 15, when the trajectory curve is a free curve, a section sweep solid is generated using an approximate section sweep generation method.

The operation of the approximate section sweep three-dimensional solid generator 11 will be described below with reference to the flowchart of FIG.

First, the approximate section sweep solid generator 11 generates a solid using a skinning method based on the arranged characteristic curves (step T1). For skinning, a rational B-spline (N
URBS (Non-Uniform Rational)
B-Spline)) curve, for example, "On Nervs: Survey, Les Piegr,
Institute of Electrical and Electronics Engineers, Computer Graphics and Applications, January 1991 ("OnNUR
BS: A Survey "(Les Piegl, IE
EE Computer Graphics & Ap
application, January 1991)).

Next, at an intermediate point between the characteristic curves on the trajectory curve, a characteristic curve is calculated by the characteristic curve calculation unit 8 (step T2), and at the same time, a three-dimensional sectional curve at the parameter point is calculated (step T2). Step T3). Then, as shown in FIG. 17, the characteristic curve at the parameter point is compared with the cross-sectional curve (step T).
4).

As means for comparing the characteristic curve and the cross-sectional curve, comparison of the curves themselves, and in the case of a NURBS curve, comparison of each control vertex may be considered. If it is not determined that the comparison is within the allowable range, the calculated characteristic curve is stored as a characteristic curve when the solid is regenerated next (step T5).
The operations after the three-dimensional generation (step T1) are performed on all the characteristic curves (step T6). When the above-described processing has been completed for all the characteristic curves, it is determined whether or not the calculated characteristic curve stored in step T5 exists (step T7). If the calculated characteristic curve exists, the stored calculated characteristic curve is newly characterized. It is added as a curve (step T8).
Using the skinning method based on the added feature curve, a solid is generated again, and the operation after step T2 is repeated. It is determined whether or not the stored calculated characteristic curve is no longer present (step T7).
If it is determined that the calculated characteristic curve stored in step 7 is no longer present, the processing is terminated, and the solid generated at that time is set as an approximate section swept solid.

After the section sweep solid is generated on each orbital curve, both ends of the solid are orbited in the section sweep solid as shown in FIG. The direction is corrected to the direction of the tangent vector at both ends corresponding to the curve (step S4 in FIG. 2).

Modification of both ends of a solid is described, for example, in "Visual Continuity", Wolfgang Baume, CAD, Vol. 20, number 6,1988
("Visual continuity", Wolf
gang Boehm, CAD Volume 20
number 6, 1988) Tangent Plain Continuous Patchwork (TANGENT)
PLANE CONTINUOUS PATCH W
(ORK).

Then, the three-dimensional synthesis unit 13 synthesizes each section sweep solid generated on the trajectory curve into one sweep solid as shown in FIG. 19 (step S in FIG. 2).
5). Here, when a curved surface is generated by a NURBS curve in the synthesis, for example, “On Nervs: Survey, Les
Piegl, Institute of Electrical and Electronics Engineers, Computer Graphics and Applications, January 1991 ("On NURBS: A Survey" (Les P
iegl, IEEE Computer Graphi
cs & Application, January
1991)) using the NURBS surface Oslo algorithm or the order increasing algorithm.
The degree of the URBS surface is made uniform to generate one NURBS surface.

As is clear from the above description, the sweep solid generating apparatus of the present invention has the following effects.

1) When calculating a characteristic curve at an arbitrary position of a trajectory curve, a characteristic curve corresponding to the type of the trajectory curve is calculated. If a coordinate transformation matrix used in the calculation cannot be uniquely defined, an appropriate plane is used. Is specified, and the coordinate transformation matrix at the parameter points is defined based on the normal vector of the plane and the tangent vector at an arbitrary parameter point of the trajectory curve. Surface generation is possible.

2) Since a section swept solid corresponding to the type of orbit curve is generated, a swept solid reflecting the characteristic of the orbit curve can be generated.

3) Since both ends of the section sweep solid are corrected in the direction of the tangent vector at both ends of the trajectory curve, if the trajectory curve is connected smoothly, the generated section sweep solid is also connected smoothly. Is done. Therefore, the synthesized sweep solid can also be a smooth curved surface. Further, it can be expressed in a general curved surface format such as a NURBS curved surface.

[0034]

According to the present invention, there is provided a sweep solid generating apparatus for calculating a characteristic curve at an arbitrary point of a trajectory curve, and arranging the calculated characteristic curve at both ends of the trajectory curve. Arranging means, a trajectory curve and a three-dimensional generation method determining means for determining whether or not to use an approximation method in the generation of a swept solid based on characteristic curves arranged at both end points of the trajectory curve, and a three-dimensional generation method determining means An interval sweep solid generating means for generating a sweep solid based on the trajectory curve and the characteristic curve when it is determined that the approximation method is not used in the generation of the sweep solid, and approximating the generation of the sweep solid by the solid generating method determining means. An approximate section sweep solid generating means for appropriately adding a characteristic curve to the trajectory curve using a characteristic curve calculating means when it is determined to use the method A curved surface matching means for adjusting the connectivity between adjacent solids in the section sweep solid obtained by the sweep solid generation means and the approximate section sweep solid generation means; Since a sweep solid is generated in accordance with the type of the orbit curve in the orbit curve section, a swept solid reflecting the characteristics of the orbit curve can be generated. In addition, since the connectivity between adjacent solids is considered in the sweep solid generated in the section, if the trajectory curves are connected smoothly, the generated sweep solid also has a smooth curved surface.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of a sweep solid generator according to the present invention.

FIG. 2 is a flowchart for explaining an operation of the sweep solid generating apparatus of FIG. 1;

FIG. 3 is an explanatory diagram of an input trajectory curve and a characteristic curve.

FIG. 4 is an explanatory diagram when a characteristic curve is arranged at both ends and an inflection point of a trajectory curve.

FIG. 5 is an explanatory diagram of a characteristic curve and a designated plane in a section.

FIG. 6 is an explanatory diagram of a characteristic curve and a designated plane in a section.

FIG. 7 is an explanatory diagram of a transformed coordinate system.

FIG. 8 is an explanatory diagram of an arrangement of a characteristic curve.

FIG. 9 is an explanatory diagram of an arrangement of a characteristic curve.

FIG. 10 is an explanatory diagram of an arrangement when the shapes of the characteristic curves are different.

FIG. 11 is an explanatory diagram for calculating a characteristic curve at a calculation destination point.

FIG. 12 is an explanatory diagram of a characteristic curve linearly interpolated at a calculation destination point.

FIG. 13 is an explanatory diagram of section sweep solid generation when a straight line is used as a trajectory curve.

FIG. 14 is an explanatory diagram of section sweep solid generation when a circular arc is used as a trajectory curve.

FIG. 15 is an explanatory diagram of section sweep solid generation when a free curve is a trajectory curve.

FIG. 16 is a flowchart for explaining the operation of the approximate section sweep three-dimensional solid generator of FIG. 1;

FIG. 17 is an explanatory diagram of a comparison between a cross-sectional curve and a trajectory curve.

FIG. 18 is a diagram for explaining an operation of the three-dimensional matching unit of FIG. 1;

FIG. 19 is a diagram showing an example of a result obtained by the sweep three-dimensional apparatus of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Control part 2 Display part 3 Keyboard part 4 Tablet part 5 File part 6 Modeling part 7 Feature curve arrangement part 8 Feature curve calculation part 9 Solid generation method discrimination part 10 Section sweep solid generation part 11 Approximate section sweep generation part 12 Matching between curved surfaces Part 13 Three-dimensional synthesis part

Continuation of the front page (56) References JP-A-1-99101 (JP, A) JP-A-3-163668 (JP, A) JP-A-4-117572 (JP, A) JP-A-4-135208 (JP) JP-A-4-263368 (JP, A) JP-A-5-94501 (JP, A) JP-A-5-250444 (JP, A) JP-A-6-301755 (JP, A) (58) Surveyed field (Int.Cl. ⁶ , DB name) G06T 17/00 JICST file (JOIS)

Claims (1)

(57) [Claims] 1. A characteristic curve calculating means for calculating a characteristic curve at an arbitrary point of a trajectory curve, a characteristic curve arranging means for arranging the calculated characteristic curve at both end points of the trajectory curve, Solid generation method determining means for determining whether or not to use an approximation method in the generation of a sweep solid based on the characteristic curves arranged at both end points of the orbital curve; and An interval sweep solid generating means for generating the swept solid based on the trajectory curve and the feature curve when it is determined that the approximation method is not used in the generation, and generating the sweep solid by the solid generating method determining means An approximate section sweep solid generating means for appropriately generating a solid by approximately adding the characteristic curve to the trajectory curve using the characteristic curve calculating means when it is determined that the approximating method is used; Section switch Curved surface matching means for adjusting connectivity between adjacent solids in the section sweep solid obtained by the loop solid generation means and the approximate section sweep solid generation means,
A three-dimensional synthesizing means for synthesizing the section sweep solid into one sweep solid.